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一类高精度TVD差分格式及其应用
引用本文:郑华盛,赵宁.一类高精度TVD差分格式及其应用[J].应用力学学报,2005,22(4):550-554.
作者姓名:郑华盛  赵宁
作者单位:1. 南昌航空航天大学,南京,210016;,南昌航空工业学院,南昌,330034
2. 南昌航空航天大学,南京,210016
基金项目:航空科学基金项目(01A52003,02A52004)和国防预研项目资助
摘    要:构造了一维非线性双曲型守恒律的一个新的高精度、高分辨率的守恒型TvD差分格式。其构造思想是:首先,将计算区间划分为若干个互不相交的小区间,再根据精度要求等分小区间,通过各细小区间上的单元平均状态变量,重构各细小区间交界面上的状态变量,并加以校正;其次,利用近似Riemann解计算细小区间交界面上的数值通量,并结合高阶Runge—Kutta TVD方法进行时间离散,得到了高精度的全离散方法。证明了该格式的TVD特性。该格式适合于使用分量形式计算而无须进行局部特征分解。通过计算几个典型的问题,验证了格式具有高精度、高分辨率且计算简单的优点。

关 键 词:双曲型守恒律  高阶精度  TVD差分格式  欧拉方程组
文章编号:1000-4939(2005)04-0550-05
收稿时间:2004-02-22
修稿时间:2004-02-222005-01-22

High Order Accurate TVD Difference Scheme with Applications
Zheng Huasheng,Zhao Ning.High Order Accurate TVD Difference Scheme with Applications[J].Chinese Journal of Applied Mechanics,2005,22(4):550-554.
Authors:Zheng Huasheng  Zhao Ning
Institution:Zheng Huasheng~
Abstract:A class of conservative TVD(Total Variation Diminishing) difference schemes with high order accuracy and resolution,is presented for 1D nonlinear hyperbolic conservation laws.The computational interval is divided into pieces of nonoverlapping sub-intervals,and then each is further subdivided into identically small intervals according to the required accuracy.Cell averaged state variables from these small intervals are used to reconstruct a high order polynomial approximation in the small interval boundaries.Furthermore the correction is introduced to prevent oscillations near discontinuities from the high-order approximation.The approximate Riemann solver is used to compute numerical fluxs on small interval boundaries,and a high-order fully discretization method is obtained by applying high-order Runge-Kutta TVD time discretization .The new scheme enables to accelerate the computation with a higher accuracy and resolution.
Keywords:hyperbolic conservation laws  high order accuracy  TVD difference scheme  Euler equations  
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